OK. Then let's define "correct" breathing methods. What makes a method "correct"? What's the difference between said correct method and someone doing, say sanchin and/or tensho from a Goju-ryu tradition (as an example)?

That's a good point, Ignatius. Bear in mind that there are a number of approaches to breathing methods by different styles, each of which thinks that it has hit on the *best* way to do breathing exercises. There are also considerations about how to do them so that no physical damage accrues from hypertension, etc., in too-exuberant practitioners. Notice Tohei's methods are of the extremely soft variety, even though he's not very forthcoming on the intricacies of the practices.

What's the correct way? Again, pretend that the fascia is a muscle like the bicep; what's the "correct" way to exercise it so that the muscle becomes strongest? Isolate it and work it in a way that gives the fibers the best incentive to become stronger and with endurance.

This is a discussion that probably belongs on QiJin, BTW. I don't think the background for the discussion has been established on AikiWeb or its archives, so to have a fruitful public discussion would require extensive discussion of background material first. Pretty arduous.